How To Calculate Expected Frequency

Expected Frequency Formula:

\[ E = \frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}} \]

Expected Frequency (E):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Expected Frequency?

Expected frequency is a statistical measure used in contingency table analysis to calculate the theoretical frequency of observations in each cell under the assumption of independence between variables. It's commonly used in chi-square tests of independence.

2. How Does The Calculator Work?

The calculator uses the expected frequency formula:

\[ E = \frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}} \]

Where:

\( E \) — Expected frequency
Row Total — Sum of all values in the row
Column Total — Sum of all values in the column
Grand Total — Sum of all values in the table

Explanation: This formula calculates what the frequency would be if there was no association between the row and column variables.

3. Importance Of Expected Frequency

Details: Expected frequencies are crucial for statistical tests like chi-square, allowing researchers to compare observed frequencies with expected frequencies to determine if variables are independent or associated.

4. Using The Calculator

Tips: Enter the row total, column total, and grand total as positive numbers. All values must be valid (greater than 0).

5. Frequently Asked Questions (FAQ)

Q1: When is expected frequency used?
A: Primarily in chi-square tests of independence to assess whether two categorical variables are related.

Q2: What if expected frequency is less than 5?
A: When expected frequencies are too small (typically <5), chi-square test results may be unreliable, and alternative tests like Fisher's exact test should be considered.

Q3: Can expected frequency be greater than observed frequency?
A: Yes, this indicates that the observed frequency is lower than what would be expected if the variables were independent.

Q4: How is expected frequency different from observed frequency?
A: Observed frequency is the actual count in the data, while expected frequency is the theoretical count assuming no association between variables.

Q5: What statistical tests use expected frequency?
A: Chi-square test of independence, chi-square goodness-of-fit test, and other categorical data analysis methods.